Question

Y=-3x² – 7x+4

Find the vertex

Answer 1

The vertex of given linear equation is

x =
`(- 7)/(6)` , y =
`(97)/(12)`

Explanation:

Given linear equation as :

y = - 3 x²- 7 x + 4

The standard equation can be written as :

y = a x² +b x + c

Now , x = ( -
`(b)/(2a)` )

So, From given equation y = - 3 x²- 7 x + 4

x = ( -
`(b)/(2a)` )

Or, x = ( -
`(- 7)/(2(-3))` )

Or, x= (
`(- 7)/(6)` )

Put the value of x in given equation

So , y = - 3 x²- 7 x + 4

Or, y =
`-3* ((-7)/(6))^(2)-7* ((-7)/(6))+4`

∴ y = -
`(49)/(12)` +
`(49)/(6)` + 4

Or , y =
`(-49 +98 +48)/(12)`

So , y =
`(97)/(12)`

Hence The vertex of given linear equation is x =
`(- 7)/(6)` , y =
`(97)/(12)` Answer